ANSWER:
[tex]2210111_3[/tex]STEP-BY-STEP EXPLANATION:
Ternary is a base 3 number system. This essentially means that it only uses 3 digits to form its numbers:
2038/3 = 679 with remainder 1
679/3 = 226 with remainder 1
226/3 = 75 with remainder 1
75/3 = 25 with remainder 0
25/3 = 8 with remainder 1
8/3 = 2 with remainder 2
2/3 = 0 with remainder 2
Therefore:
[tex]2038_{10}=2210111_3_{}[/tex]